Strong global attractors for nonclassical diffusion equation with fading memory

摘要

Based on semigroup theory and the method of contractive function, we prove the existence of global attractors for a nonclassical diffusion equation with fading memory in the space H 2 ( Ω ) ∩ H 0 1 ( Ω ) × L μ 2 ( R + ; H 2 ( Ω ) ∩ H 0 1 ( Ω ) ) $H^{2}(Omega)cap H_{0}^{1}(Omega) imes L_{mu}^{2}(mathbb{R}^{+};H^{2}(Omega)cap H_{0}^{1}(Omega))$ , when the nonlinearity satisfies arbitrary polynomial growth.